Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.28262 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918527643942912 |
|---|---|
| author | Chen, Xiaojuan Tang, Shengyu Wang, Sinan |
| author_facet | Chen, Xiaojuan Tang, Shengyu Wang, Sinan |
| contents | This paper studies the core problems in the $L_p$ dual Brunn-Minkowski theory, encompassing the $L_p$ Minkowski problem and $L_p$ Brunn-Minkowski inequality for dual quermassintegrals. For the case $0<p<q\leq n$, we establish $C^0$ estimates for the $L_p$ dual Minkowski problem without symmetric assumptions, thereby resolving a related problem proposed by Böröczky-Chen-Liu-Saroglou in the smooth sense. We further prove the uniqueness of smooth solutions under appropriate conditions, provided the density function is sufficiently close to a constant in the Hölder norm. Finally, exploiting the fact that the uniqueness of the Minkowski type problem is equivalent to the validity of the Brunn-Minkowski inequality in a certain sense, we study the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals for origin-symmetric convex bodies with $p<q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28262 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L_p$ Minkowski problem and Brunn-Minkowski inequality for dual quermassintegrals Chen, Xiaojuan Tang, Shengyu Wang, Sinan Analysis of PDEs This paper studies the core problems in the $L_p$ dual Brunn-Minkowski theory, encompassing the $L_p$ Minkowski problem and $L_p$ Brunn-Minkowski inequality for dual quermassintegrals. For the case $0<p<q\leq n$, we establish $C^0$ estimates for the $L_p$ dual Minkowski problem without symmetric assumptions, thereby resolving a related problem proposed by Böröczky-Chen-Liu-Saroglou in the smooth sense. We further prove the uniqueness of smooth solutions under appropriate conditions, provided the density function is sufficiently close to a constant in the Hölder norm. Finally, exploiting the fact that the uniqueness of the Minkowski type problem is equivalent to the validity of the Brunn-Minkowski inequality in a certain sense, we study the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals for origin-symmetric convex bodies with $p<q$. |
| title | $L_p$ Minkowski problem and Brunn-Minkowski inequality for dual quermassintegrals |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.28262 |